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Identifier
Values
=>
Cc0002;cc-rep
[2]=>0 [1,1]=>0 [3]=>0 [2,1]=>1 [1,1,1]=>1 [4]=>1 [3,1]=>2 [2,2]=>1 [2,1,1]=>1 [1,1,1,1]=>1 [5]=>2 [4,1]=>3 [3,2]=>1 [3,1,1]=>1 [2,2,1]=>3 [2,1,1,1]=>3 [1,1,1,1,1]=>3 [6]=>5 [5,1]=>6 [4,2]=>3 [4,1,1]=>3 [3,3]=>5 [3,2,1]=>5 [3,1,1,1]=>5 [2,2,2]=>3 [2,2,1,1]=>3 [2,1,1,1,1]=>3 [1,1,1,1,1,1]=>3 [7]=>8 [6,1]=>9 [5,2]=>5 [5,1,1]=>5 [4,3]=>3 [4,2,1]=>7 [4,1,1,1]=>7 [3,3,1]=>9 [3,2,2]=>3 [3,2,1,1]=>3 [3,1,1,1,1]=>3 [2,2,2,1]=>7 [2,2,1,1,1]=>7 [2,1,1,1,1,1]=>7 [1,1,1,1,1,1,1]=>7 [8]=>14 [7,1]=>15 [6,2]=>10 [6,1,1]=>10 [5,3]=>7 [5,2,1]=>12 [5,1,1,1]=>12 [4,4]=>14 [4,3,1]=>10 [4,2,2]=>14 [4,2,1,1]=>14 [4,1,1,1,1]=>14 [3,3,2]=>10 [3,3,1,1]=>10 [3,2,2,1]=>10 [3,2,1,1,1]=>10 [3,1,1,1,1,1]=>10 [2,2,2,2]=>14 [2,2,2,1,1]=>14 [2,2,1,1,1,1]=>14 [2,1,1,1,1,1,1]=>14 [1,1,1,1,1,1,1,1]=>14 [9]=>21 [8,1]=>22 [7,2]=>16 [7,1,1]=>16 [6,3]=>12 [6,2,1]=>18 [6,1,1,1]=>18 [5,4]=>10 [5,3,1]=>15 [5,2,2]=>10 [5,2,1,1]=>10 [5,1,1,1,1]=>10 [4,4,1]=>22 [4,3,2]=>14 [4,3,1,1]=>14 [4,2,2,1]=>22 [4,2,1,1,1]=>22 [4,1,1,1,1,1]=>22 [3,3,3]=>12 [3,3,2,1]=>18 [3,3,1,1,1]=>18 [3,2,2,2]=>14 [3,2,2,1,1]=>14 [3,2,1,1,1,1]=>14 [3,1,1,1,1,1,1]=>14 [2,2,2,2,1]=>22 [2,2,2,1,1,1]=>22 [2,2,1,1,1,1,1]=>22 [2,1,1,1,1,1,1,1]=>22 [1,1,1,1,1,1,1,1,1]=>22 [10]=>32 [9,1]=>33 [8,2]=>26 [8,1,1]=>26 [7,3]=>21 [7,2,1]=>28 [7,1,1,1]=>28 [6,4]=>18 [6,3,1]=>24 [6,2,2]=>18 [6,2,1,1]=>18 [6,1,1,1,1]=>18 [5,5]=>32 [5,4,1]=>22 [5,3,2]=>20 [5,3,1,1]=>20 [5,2,2,1]=>22 [5,2,1,1,1]=>22 [5,1,1,1,1,1]=>22 [4,4,2]=>26 [4,4,1,1]=>26 [4,3,3]=>18 [4,3,2,1]=>18 [4,3,1,1,1]=>18 [4,2,2,2]=>26 [4,2,2,1,1]=>26 [4,2,1,1,1,1]=>26 [4,1,1,1,1,1,1]=>26 [3,3,3,1]=>24 [3,3,2,2]=>18 [3,3,2,1,1]=>18 [3,3,1,1,1,1]=>18 [3,2,2,2,1]=>18 [3,2,2,1,1,1]=>18 [3,2,1,1,1,1,1]=>18 [3,1,1,1,1,1,1,1]=>18 [2,2,2,2,2]=>26 [2,2,2,2,1,1]=>26 [2,2,2,1,1,1,1]=>26 [2,2,1,1,1,1,1,1]=>26 [2,1,1,1,1,1,1,1,1]=>26 [1,1,1,1,1,1,1,1,1,1]=>26 [11]=>45 [10,1]=>46 [9,2]=>38 [9,1,1]=>38 [8,3]=>32 [8,2,1]=>40 [8,1,1,1]=>40 [7,4]=>28 [7,3,1]=>35 [7,2,2]=>28 [7,2,1,1]=>28 [7,1,1,1,1]=>28 [6,5]=>26 [6,4,1]=>32 [6,3,2]=>20 [6,3,1,1]=>20 [6,2,2,1]=>32 [6,2,1,1,1]=>32 [6,1,1,1,1,1]=>32 [5,5,1]=>46 [5,4,2]=>24 [5,4,1,1]=>24 [5,3,3]=>26 [5,3,2,1]=>26 [5,3,1,1,1]=>26 [5,2,2,2]=>24 [5,2,2,1,1]=>24 [5,2,1,1,1,1]=>24 [5,1,1,1,1,1,1]=>24 [4,4,3]=>32 [4,4,2,1]=>40 [4,4,1,1,1]=>40 [4,3,3,1]=>32 [4,3,2,2]=>32 [4,3,2,1,1]=>32 [4,3,1,1,1,1]=>32 [4,2,2,2,1]=>40 [4,2,2,1,1,1]=>40 [4,2,1,1,1,1,1]=>40 [4,1,1,1,1,1,1,1]=>40 [3,3,3,2]=>20 [3,3,3,1,1]=>20 [3,3,2,2,1]=>32 [3,3,2,1,1,1]=>32 [3,3,1,1,1,1,1]=>32 [3,2,2,2,2]=>32 [3,2,2,2,1,1]=>32 [3,2,2,1,1,1,1]=>32 [3,2,1,1,1,1,1,1]=>32 [3,1,1,1,1,1,1,1,1]=>32 [2,2,2,2,2,1]=>40 [2,2,2,2,1,1,1]=>40 [2,2,2,1,1,1,1,1]=>40 [2,2,1,1,1,1,1,1,1]=>40 [2,1,1,1,1,1,1,1,1,1]=>40 [1,1,1,1,1,1,1,1,1,1,1]=>40 [12]=>65 [11,1]=>66 [10,2]=>57 [10,1,1]=>57 [9,3]=>50 [9,2,1]=>59 [9,1,1,1]=>59 [8,4]=>45 [8,3,1]=>53 [8,2,2]=>45 [8,2,1,1]=>45 [8,1,1,1,1]=>45 [7,5]=>42 [7,4,1]=>49 [7,3,2]=>35 [7,3,1,1]=>35 [7,2,2,1]=>49 [7,2,1,1,1]=>49 [7,1,1,1,1,1]=>49 [6,6]=>65 [6,5,1]=>47 [6,4,2]=>37 [6,4,1,1]=>37 [6,3,3]=>65 [6,3,2,1]=>49 [6,3,1,1,1]=>49 [6,2,2,2]=>37 [6,2,2,1,1]=>37 [6,2,1,1,1,1]=>37 [6,1,1,1,1,1,1]=>37 [5,5,2]=>57 [5,5,1,1]=>57 [5,4,3]=>33 [5,4,2,1]=>37 [5,4,1,1,1]=>37 [5,3,3,1]=>47 [5,3,2,2]=>33 [5,3,2,1,1]=>33 [5,3,1,1,1,1]=>33 [5,2,2,2,1]=>37 [5,2,2,1,1,1]=>37 [5,2,1,1,1,1,1]=>37 [5,1,1,1,1,1,1,1]=>37 [4,4,4]=>45 [4,4,3,1]=>53 [4,4,2,2]=>45 [4,4,2,1,1]=>45 [4,4,1,1,1,1]=>45 [4,3,3,2]=>37 [4,3,3,1,1]=>37 [4,3,2,2,1]=>53 [4,3,2,1,1,1]=>53 [4,3,1,1,1,1,1]=>53 [4,2,2,2,2]=>45 [4,2,2,2,1,1]=>45 [4,2,2,1,1,1,1]=>45 [4,2,1,1,1,1,1,1]=>45 [4,1,1,1,1,1,1,1,1]=>45 [3,3,3,3]=>65 [3,3,3,2,1]=>49 [3,3,3,1,1,1]=>49 [3,3,2,2,2]=>37 [3,3,2,2,1,1]=>37 [3,3,2,1,1,1,1]=>37 [3,3,1,1,1,1,1,1]=>37 [3,2,2,2,2,1]=>53 [3,2,2,2,1,1,1]=>53 [3,2,2,1,1,1,1,1]=>53 [3,2,1,1,1,1,1,1,1]=>53 [3,1,1,1,1,1,1,1,1,1]=>53 [2,2,2,2,2,2]=>45 [2,2,2,2,2,1,1]=>45 [2,2,2,2,1,1,1,1]=>45 [2,2,2,1,1,1,1,1,1]=>45 [2,2,1,1,1,1,1,1,1,1]=>45 [2,1,1,1,1,1,1,1,1,1,1]=>45 [1,1,1,1,1,1,1,1,1,1,1,1]=>45
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Description
The number of characters of the symmetric group whose value on the partition is even.
References
[1] Miller, A. R. Note on parity and the irreducible characters of the symmetric group arXiv:1708.03267
Code
def statistic(la):
    s = SymmetricFunctions(ZZ).s()
    p = SymmetricFunctions(ZZ).p()
    P = Partitions(la.size())
    r = P.cardinality()
    res = [0]*r    
    for i, (mu, v) in enumerate(s(p(la))):
            res[i] = v
    return len([1 for e in res if is_even(e)])

Created
Aug 12, 2017 at 11:37 by Martin Rubey
Updated
Aug 12, 2017 at 11:37 by Martin Rubey